I heard Tim Van Eyken sing this at "Not the White Horse Folk Club" in Beverley.

http://www.timvaneyken.co.uk/

His was a mixture of the two versions above which went something like this:

1. Oh, I have eaten him, what did I eat?
I ate the head of the mallard.
Head head and toe and toe, toe nibbins'n all,
It all went into the pellagio [stomach]
Oh most beautiful head of the mallard.

You may find the song on one of his recordings if you want the tune.